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Theorem alrimii 32423
 Description: A lemma for introducing a universal quantifier, in inference form. (Contributed by Giovanni Mascellani, 30-May-2019.)
Hypotheses
Ref Expression
alrimii.1
alrimii.2
alrimii.3
alrimii.4
Assertion
Ref Expression
alrimii
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem alrimii
StepHypRef Expression
1 alrimii.1 . . 3
2 alrimii.2 . . . 4
3 alrimii.3 . . . 4
42, 3sylibr 217 . . 3
51, 4alrimi 1975 . 2
6 nfsbc1v 3275 . . 3
7 alrimii.4 . . 3
8 sbceq2a 3267 . . 3
96, 7, 8cbval 2127 . 2
105, 9sylib 201 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189  wal 1450  wnf 1675  wsbc 3255 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-sbc 3256 This theorem is referenced by: (None)
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